Okay so I've seen that some not all power supplies have a positive and negative side for the voltag output and in addition have a common ground connection, exactly what is that used for?

Ohhhh ? like to show an example of one that doesnt :)
All the many and varied PSU's I have worked with over the last 40 years all have a positive and negative output. bit difficult to complete a circuit without a negative rail ;)
Some may also have a ground/chassis connection and that connection may or may not be commoned with the negative

Lol let me explain that differently, all of the power suPplies I've seen have a positive and a negative, and some also have standalone ground connection or common ground, so what is it exactly? I know what ground is but what is a "common" ground for?

Lol let me explain that differently, all of the power suPplies I've seen have a positive and a negative, and some also have standalone ground connection or common ground, so what is it exactly? I know what ground is but what is a "common" ground for?

Some what, an op-amp circuit. The positive and negative feed the power for the op amp while the common ground, is used to ground the rest of the components that may be used, such as a function generator or oscilloscope, now is it necessary to use common ground for everything else? Or can we just use the low Potential or - for everything?

in that case its a little bit different, as its not the standard + and - rails where the ground and/or chassis is connected to the negative. Thats a split rail supply. Its specifically designed for components that need to work with a positive and negative rail, say +12 and -12 Volts. Other parts of the circuit may well just use the +12v and 0V rails

Now that 0V rail may or may not be connected to chassis ground. Thats really up to the designer of the circuit and what they are trying to achieve.